A topological property of the common fixed points set of two multivalued operators. (English) Zbl 1169.54022
Summary: Let \((X,d)\) be a complete metric space and absolute retract for metric spaces. We prove that the common fixed points set of two multivalued operators defined on \(X\), which have the selection property and satisfy a contraction type condition, is an absolute retract for metric spaces.
MSC:
54H25 | Fixed-point and coincidence theorems (topological aspects) |
54C60 | Set-valued maps in general topology |
47H04 | Set-valued operators |
47H10 | Fixed-point theorems |
Keywords:
multivalued operator; fixed point; common fixed point; absolute retract; selection propertyReferences:
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